How large is your tank and what is the wattage and spectrum of your lightbulb? Amazon sword is at least a medium-light plant and it will barely survive under standard (meaning low) lighting or it will die under such conditions. I also have a couple Amazon Swords in my 30G tank that has a 20W bulb. To tell you the truth, while the plants are alive, they do BARELY survive in my tank. They grow VERY slowly and every once in a while some leaves decay. This is because my lighting is too low in my tank for a plant like this. I suppose the same is happening in your case.
Decay of leaves is normal in a plant's life cycle. Even in high-light planted tanks plants have decaying leaves from time to time, but these plants are not dying but doing very well. However, like I said, under a standard light, the plant will eventually die, or at best it will continue to barely survive (such as in my case).